How do you calculate the radius of a star?

How do you calculate the radius of a star?

I have to list the steps required and explain how those steps are determined.How do you calculate the radius of a star?Calculating the Radius of a Star



Calculating a star's radius is a somewhat lengthy process. You have to put together many tools that you have developed in various SkyServer projects. Even the largest star is so far away that it appears as a single point from the surface of the Earth - its radius cannot be measured directly. Fortunately, understanding a star's luminosity provides you with the tools necessary to calculate its radius from easily measured quantities.



A star's luminosity, or total power given off, is related to two of its properties: its temperature and surface area. If two stars have the same surface area, the hotter one will give off more radiation. If two stars have the same temperature, the one with more surface area will give off more radiation. The surface area of a star is directly related to the square of its radius (assuming a spherical star).



The luminosity of a star is given by the equation



L = 4pR2s T4,



Where L is the luminosity in Watts, R is the radius in meters, s is the Stefan-Boltzmann constant

(5.67 x 10-8 Wm-2K-4), and T is the star's surface temperature in Kelvin.



The temperature of a star is related to its b-v magnitude.



for b-v value go to link



The calculation is actually somewhat easier if we try to find the ratio of another star's radius to that of our Sun. Let Ls be the luminosity of the Sun, L be the luminosity of another star, Ts be the temperature of the Sun, T be the temperature of the other star, Rs be the radius of the Sun, and R be the radius of the other star.



We can then write the ratio of their luminosities as



L/Ls = (4pR2sT4)/(4pRs2sTs4) = (R/Rs)2(T/Ts)4



Solving for the ratio R/Rs yields



R/Rs = (Ts/T)2(L/Ls)1/2



The temperatures can be found approximately from the table above by looking at the B-V values. To find the ratio L/Ls, we can use the absolute magnitudes of the stars. The magnitude scale is a logarithmic scale. For every decrease in brightness of 1 magnitude, the star is 2.51 times as bright. Therefore, L/Ls can be found from the equation



L/Ls = 2.51Dm,



where Dm = ms - m



Let's look at the star Sirius. It has visual magnitude of -1.44, B-V of .009, and a parallax of 379.21 milli arc seconds. Finding its distance from its parallax yields



d = 1/p = 1/.37921 = 2.63 parsecs.



Its absolute magnitude is



M = m - 5 log d + 5 = -1.44 - 5 log (2.63) + 5 = 1.46



We know the temperature of the Sun is 5800K. From the chart, the temperature of Sirius is about 9500K. Our Sun has an absolute magnitude of 4.83. The difference in magnitude is 3.37. Putting everything together yields



R/Rs = (5800/9500)2(2.5123.37)1/2 = 1.76



Sirius has a radius approximately 1.76 times that of our Sun!How do you calculate the radius of a star?Both the previous answers are pretty much spot on - although awais seems to make it more complicated than necessary.



Basically you need to know a star's luminosity, temperature and distance.

If the star isn;t too far away, you can use a parallax observation to get distance.

Then you measure how much light we received from the star every second, and together with the distance, this gives luminosity - which is how much total energy is emitted every second.

Taking a spectrum allows you to determine the temperature of the star.



Then, because stars are essentially blackbodies - you apply the Stefan_Boltzmann law: L = 4 pi R^2 sigma T^4

since pi and sigma are constants and you have measured L and T, you can calculate R.



If the star is more than a few hundred light years away, parallax is no use - and measuring distance is harder.



However, then we can use the width of the absorption lines in the spectrum to estimate size using MKK luminosity classes.

http://astronomy.swin.edu.au/cosmos/M/Mo鈥?/a>

In this case you just need the spectrum and a HR diagram to get the size - but the estimate of radius is not so precise.How do you calculate the radius of a star?This is a rather difficult process. Most stars are too far away to directly observe the radius. Only a few nearby giant stars have had their radii directly measured.



Most of the time you estimate the radius of a star based on its luminosity and temperature. Using the black-body radiation formula you can figure out the radius.



L = pi * 4 * R^2 * sigma * T^4



where sigma = 5.67e-8 (Stefan-Boltzmnan constant)

L is luminosity

R is radius

T is temperature